Spatio-temporal probabilistic modeling based on Gaussian mixture models and neural gas theory for prediction of criminal activity

Abstract

Criminal risk models are used to assist security forces both in the identification of zones with high of criminal activity for better resource allocation and prediction of future criminal events for the prevention of new crimes. In this sense, spatio-temporal models are widely employed by their capacity of characterizing the criminal risk inside of a zone of interest and updating the model to new crime data. This paper improves an existing method based on spatio-temporal probabilistic risk functions. The spatial probabilistic characterization uses geo-referenced information of criminal incidents related to public services to approximate a risk function based on a Gaussian Mixture Model (GMM). The temporal characterization is supported by Importance Sampling methods and Neural Gas theory to incorporate the information from new measurements, in a recursive manner, updating the spatial probabilistic risk function. Finally, we propose a prediction scheme for criminal activity that also uses Neural Gas Theory, in conjunction with hypothetical future criminal events sampled from a GMM that characterizes the spatial distribution associated with recent criminal activity. The time index related to each hypothetical future crime event is probabilistically characterized using an exponential distribution. Results using real data and the defined performance indexes show an improvement both in the temporal updating as well as the proposed prediction approach.